skip to main content

SciTech ConnectSciTech Connect

Title: Transient and chaotic low-energy transfers in a system with bistable nonlinearity

The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to a lightweight mass by means of a spring with both cubic nonlinear and negative linear components is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator, excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics evolves solely in-well. The description of the former dissipative phenomenon is provided in a two-dimensional projection of the phase space, where transitions between in-well and cross-well oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second mechanism is described in terms of secondary limiting phase trajectories of the nonlinear attachment under certain resonance conditions. The analytical treatment of the two aformentioned low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully validate our analytical predictions.
Authors:
 [1] ;  [2] ; ;  [3]
  1. Department of Structural and Geotechnical Engineering, SAPIENZA University of Rome, Rome (Italy)
  2. Institute of Chemical Physics, RAS, Moscow (Russian Federation)
  3. College of Engineering, University of Illinois at Urbana–Champaign, Champaign, Illinois 61820 (United States)
Publication Date:
OSTI Identifier:
22402557
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTIC FUNCTIONS; ASYMPTOTIC SOLUTIONS; CHAOS THEORY; COMPUTERIZED SIMULATION; ENERGY TRANSFER; MASS; NONLINEAR PROBLEMS; OSCILLATIONS; OSCILLATORS; PHASE SPACE; TRANSIENTS; TWO-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL SYSTEMS